Understanding electron and ion heating phenomenon in capacitively coupled radio-frequency plasma discharges is vital for many plasma processing applications. In this article, using particle-in-cell simulation technique we investigate the collisionless argon discharge excited by temporally asymmetric sawtooth-like waveform. In particular, a systematic study of the electric field nonlinearity and field reversal phenomenon by varying the number of harmonics and its effect on electron and ion heating is performed. The simulation results predict higher harmonics generation and multiple field reversal regions formation with an increasing number of harmonics along with the local charge separation and significant displacement current outside sheath region. The field reversal strength is greater during the expanding phase of the sheath edge in comparison to its collapsing phase causing significant ion cooling. The observed behavior is associated with the electron fluid compression/rarefaction and electron inertia during expanding and collapsing phase respectively.